Preheat the oven to 180°C (350°F). Grease a 9-inch round cake pan.
Peel and core the apples, then slice them thinly. Set aside.
In a mixing bowl, whisk together the eggs, granulated sugar, and vanilla extract until well combined.
In another bowl, mix the flour, baking powder, and salt. Gradually add this dry mixture to the egg mixture, stirring until smooth.
Slowly pour in the milk and melted butter, mixing until fully incorporated.
Fold in the sliced apples gently until they are well coated with the batter.
Pour the mixture into the prepared cake pan, spreading it evenly.
Bake in the preheated oven for 40-45 minutes, or until the top is golden and a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.
Once cooled, dust the top with powdered sugar before serving.